{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T11:46:20Z","timestamp":1753875980904,"version":"3.41.2"},"reference-count":31,"publisher":"Oxford University Press (OUP)","issue":"4","license":[{"start":{"date-parts":[[2024,8,5]],"date-time":"2024-08-05T00:00:00Z","timestamp":1722816000000},"content-version":"vor","delay-in-days":42,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2024,6,24]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>The way in which a social network is generated, in terms of how individuals attach to each other, determines the properties of the resulting network. Here, we study an intuitively appealing \u2018friend of a friend\u2019 model, where a network is formed by each newly added individual attaching first to a randomly chosen target and then to nq\u2009\u2a7e\u20091 randomly chosen friends of the target, each with probability 0&amp;lt;q\u2a7d\u20091. We revisit the master equation of the expected degree distribution for this model, providing an exact solution for the case when nq allows for attachment to all of the chosen target\u2019s friends [a case previously studied by Bhat et al. (2016, Phys. Rev. E, 94, 062302)], and demonstrating why such a solution is hard to obtain when nq is fixed [a case previously studied by Levens et al. (2022, R. Soc. Open Sci., 9, 221200)]. In the case where attachment to all friends is allowed, we also show that when q&amp;lt;q*\u22480.5671, the expected degree distribution of the model is stationary as the network size tends to infinity. We go on to look at the clustering behaviour and the triangle count, focusing on the cases where nq is fixed.<\/jats:p>","DOI":"10.1093\/comnet\/cnae032","type":"journal-article","created":{"date-parts":[[2024,8,6]],"date-time":"2024-08-06T00:39:32Z","timestamp":1722904772000},"source":"Crossref","is-referenced-by-count":0,"title":["Properties of the \u2018friend of a friend\u2019 model for network generation"],"prefix":"10.1093","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4762-8914","authenticated-orcid":false,"given":"Tiffany Y Y","family":"Lo","sequence":"first","affiliation":[{"name":"Department of Mathematics, Uppsala University , 752 37 Uppsala, Sweden"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Watson","family":"Levens","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Dar es Salaam , 35065 Dar es Salaam, Tanzania"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"David J T","family":"Sumpter","sequence":"additional","affiliation":[{"name":"Division of Systems and Control, Department of Information Technology, Uppsala University , 751 05 Uppsala, Sweden"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2024,8,5]]},"reference":[{"key":"2024080600392833200_cnae032-B1","doi-asserted-by":"crossref","first-page":"509","DOI":"10.1126\/science.286.5439.509","article-title":"Emergence of scaling in random networks","volume":"286","author":"Barab\u00e1si","year":"1999","journal-title":"Science"},{"key":"2024080600392833200_cnae032-B2","doi-asserted-by":"crossref","first-page":"440","DOI":"10.1038\/30918","article-title":"Collective dynamics of \u2018small-world\u2019 networks","volume":"393","author":"Watts","year":"1998","journal-title":"Nature"},{"key":"2024080600392833200_cnae032-B3","doi-asserted-by":"crossref","first-page":"042806","DOI":"10.1103\/PhysRevE.90.042806","article-title":"Triadic closure as a basic generating mechanism of communities in complex networks","volume":"90","author":"Bianconi","year":"2014","journal-title":"Phys. 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